Abstract
A large number of observables can be constructed from differential decay rate based on the polarization of final state while considering decay of a neutral meson (P^{0} text { or } {bar{P}}^{0}) to two vector particles. But all of these observables are not independent to each other since there are only a few independent theoretical parameters controlling the whole dynamics and therefore various relations among observables emerge. In this paper, we have studied the behaviour of observables for neutral meson decaying to two vectors in presence of T and C!P T violations in mixing accompanied by both direct and indirect C!P violations. We have expressed all of the fourteen unknown theoretical parameters for this scenario in terms observables only and constructed the complete set of thirty four relations among observables whose violation would signify the existence of some new Physics involving direct violation of C!P T. In addition, using this formalism we have studied three special cases too: (a) SM scenario, (b) SM plus direct C!P violation (c) SM plus T and C!P T violation in mixing.
Highlights
Theoretical frameworkLet us first briefly review the most general formalism incorporating CP T and T violation for P0 − P 0mixing, which has already been discussed in Refs. [2,64,73]
(Sect. 2), we briefly describe the theoretical formalism for CP T violation in P0 − P 0 mixing and express the time dependent differential decay rates of P0 and P 0 in terms of the mixing parameters
We have studied the behaviour of observables for neutral meson decaying to two vectors in the presence of T, CP and CP T violation in mixing as well as CP violation in decay
Summary
Let us first briefly review the most general formalism incorporating CP T and T violation for P0 − P 0mixing, which has already been discussed in Refs. [2,64,73]. In the flavour basis (P0, P 0), the mixing Hamiltonian can be expressed in terms of two 2 × 2 Hermitian matrices, namely mass-matrix M and decay-matrix , as M − (i/2). The mass eigenstates or physical states |PL and |PH are the eigenvectors of the mixing Hamiltonian M − (i/2) and they can be expressed as linear combinations of the flavour eigenstates (|P0 and |P0 ) as follows:. It should be noted that the physical states are not orthogonal in general since the mixing matrix is non-Hermitian. Incorporating the mixing, the time dependent decay rates (P0(t) → f ) and (P0(t) → f ) can be expressed as:. + 2Re eiφ∗ cos θ sin θ ∗A∗f Af + sin( Mt) 2Im − cos θ ∗|Af |2 + eiφ∗ sin θ ∗A∗f Af
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